A science question

I have a science question. The Earth, as old as it is, is still quite hot in the middle. From what I understand, the crust is roughly 2-10 miles thick and the mantle is hundreds of miles thick before we get to the core. Volcanic activity shows us a hint of how hot be the innards. My question is this: Why does it take a planet so long to cool off? Anything baked in a ceramic kiln may glow red for a minute, yet may be cool in a day. If the earth is as old as they say, why is is still so darned hot on the inside?
Does anyone have an approximation of when the core will be cool to the touch? (Put in Geology?)This message has been edited by Phatboy, 01-26-2005 05:06 AM

Thread moved here from the Proposed New Topics forum.

IIRC there are three processes at work. First, radioactivity provides some heat but probably less than many claimed in the past. Second, the earth's gravity is still trying to compress us into a smaller ball. This heats up the interior as it's squeezed. The third mechanism is probably the smallest contributor and that is solar radiation heating the surface.But hopefully someone with far more knowledge than I have will give you the real answers.

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Aslan is not a Tame Lion

I really don't know much about this, but wouldn't surface area have something to do with the rate of cooling?Also, how hot the item was to begin with, density, etc?

You missed an obvious one (although it's contribution may be small). Phase changes - as rock goes from molten to solid it will give up heat. IIRC there are some exothermic chemical reactions going on down there, too. And of course the outer layers of the planet act as insulation to some degree.

As I understand it, about half the heat comes from radioactive decay - potassium-40 and uranium, mostly. The other half comes from gravitational potential energy being turned to heat as heavier stuff settles toward the middle, and from the heat of crystallization released as the liquid of the outer core crystallizes onto the inner core.I don't know when it'll be down to lukewarm, and I'm not waiting around to find out...

I thought about adding that but I imagine that will actually turn out to be something of a wash. While it will release heat to the cooler layers surrounding the core, it will not and cannot transfer heat to the hotter core.I was trying to stick to those things that could heat the interior. The surface warming actually probably should have been included in the same category as phase changes, increasing the temperature and so insulating the core. Afterall, as two objects approach equlibrium it gets increasingly harder to transfer heat.

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Aslan is not a Tame Lion

The other mechanism that's listed in most discussions is fractionation; heavier elements are still sinking ot the core and that si another source of heat.

The rate at which a body can radiate heat is a function of its surface area, and the rate at which a body can cool is a function of the ratio of surface area to volume. A sphere is the most efficient shape for conserving heat, which means spheres cool more slowly than any other object.But I think your issue is actually one of scale. You mention the time it takes a ceramic to cool from red hot, but a ceramic has a very high surface area to volume because it is so small, even if you're making marbles. For example, a one inch radius clay sphere has a surface area of 4πr² or 12.6 in², and a volume of 4πr³/3 or 4.2 in³, for a surface area to volume ratio of 3. The earth has a surface area of 8.1x10¹⁷ in² and a volume of 6.8x10²⁵ in³, for a surface area to volume ratio of 1.2x10^-8, which is orders of magnitude smaller than for your clay sphere. Naturally it will take much longer to cool.But Lord Kelvin calculated that it would take the earth only about 20 million years to cool from a molton state to its current state (he took the increasing temperature with depth into account by obtaining measurements from deep mines), and while I can offer no precise figure for how long Kelvin might have thought it would have cooled completely, certainly it wouldn't have been on the order of billions of years. The reason the earth hasn't yet fully cooled after 4.5 billion years is due to the contributions others have mentioned, radioactivity primary among them. Radioactivity was unknown to Kelvin, though it's contribution was uncovered not long before his death.Here's an example from the real world. When you take a tour of the Hoover Dam you learn quite a bit about its construction. Given the size and thickness of the dam, had they just layed the concrete and allowed it to cool naturally it would have taken a couple centuries. Not wanting to wait that long, they included water pipes to circulate cold water in every concrete segment. In other words, big objects take a long time to cool.--PercyThis message has been edited by Percy, 01-26-2005 11:30 AM

Dont the internal motions of the plannet also create a whole lot of friction,and thus heat? as well as setting up the dynamo effect that created the earth's magnetic field.This message has been edited by ohnhai, 01-26-2005 11:00 AM

The Earth is so hot on the inside because heat is still being generated there, and because the mechanisms for transporting heat away from the Earth take time. I have no idea when, if ever, the core will be cool to the touch; we may be engulfed by the Sun turning into a red giant (in five billion or so years) before the core cools.There's a long and interesting history of the answer to your questions.Isaac Newton speculated on how long it would take a globe of red-hot iron, the size of the Earth, to cool. He pretty much guessed, and came up with 50,000 years.Georges-Louis Leclerc, Comte de Buffon, made an attempt in the late 1700's. He had a foundry build him iron spheres of different diameters (1/2 inch to 5 inches). He heated them to white heat and measured the cooling time. He found a roughly linear relationship between diameter and cooling rate. Assuming the Earth was like an iron sphere and extrapolating to the Earth's size, he came up with 96,670 years (the precision is obviously not justified). Later he repeated the experiment with rock spheres and including the ffect of the Sun's heat, and modified his result to 74,832 years. This wildly wrong result was actually very important in the development of modern science and geology. From "The Age of the Earth", G. Brent Dalrymple, Stanford University Press, 1991, page 31:

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Buffon's major contribution to science, however, was much more important and lasting than his several ages for the Earth. Buffon believed and demonstrated that nature was rational and could be understood in terms of ordinary physical processes force, motion, chemical reaction, heat, and other forms of energy operating over geologic time. Invoking unique, supernatural, or extraordinary causes to explain natural history was to Buffon both unnecessary and unproductive. Thus, Buffon was the first to construct a history of the Earth based on the application of observable processes to explain the effects produced by like processes in the past. He also was the first to apply laboratory experimentation to the problem of the age of the Earth, and in doing so became one of the founders of geophysics. Finally, Buffon clearly separated the appropriate roles of theology and science in explaining nature science was perfectly capable of answering the questions of how and when; the question of why was reserved for theology. Although Buffon's age for the Earth and much of his detailed history of the planet as set forth in Epochs are now known to be incorrect, the techniques he developed for deciphering Earth history through application of the law of cause and effect are a keystone of the modern scientific method.

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The most famous early result about the Earth's cooling was from William Thomson (later Lord Kelvin) in 1862. He used measured properties of rocks, measurements of temperature from wells and mines, and the relatively new science of thermodynamics to calculate a cooling time of 98 million years. He realized that his data was inadequate, and estimated that the cooling time was no less than 20 million years and no more than 400 million years.This was a tremendous problem for geologists and "evolutionists". Lord Kelvin was the Einstein of his day, and his results and pronouncements were held in high repute. But the results of geologists studying the Earth and "evolutionists" studying the fossil record strongly suggested the Earth was much older. There were lively debates.Later papers by others refined Kelvin's calculations, and probably the "best" estimate based on the assumptions and knowledge of the day was 24 million years, by Clarence King in 1893.So, we can see that if the Earth is as old as we say it is today, then there must be some source of heat other than the influx of solar energy and the initial heat content when the Earth formed. And that is ... radioactivity. Well, mostly. Dalrymple puts it well on pages 46-47:

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But the most serious flaw in Kelvin's method is that its basic assumptions are invalid. The thermal budget of the Earth is far more complex than Kelvin, King, Chamberlain, or any nineteenth-century scientist could possibly have imagined. One complication is that there are far more sources of heat within the Earth than were known in Kelvin's time. One important source, recognized by Kelvin, is primordial, i.e. heat left over from the formation of the Earth. Radioactivity, gravitational energy from compaction, chemical energy from the segregation of the iron—nickel core, and mechanical energy from meteoritic impacts during the period that the Earth was still sweeping up large quantities of material from its orbital path all contributed to this primordial heat. These sources probably generated enough heat to raise the temperature of the outer part of the Earth to near the melting point within 100 to 200 Ma of its formation. Much of this primordial heat has not yet escaped from the Earth.

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A second and probably the most important source of continuing heat production is radioactivity. This heat is generated by the radioactive decay of primarily uranium, thorium, and potassium contained in the rocks of the Earth. Although the exact distribution of these radioactive elements within the Earth is not well known, there is no problem in constructing reasonable models that attribute most or even all of the heat now flowing outward from the Earth to radioactive decay.

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In addition to primordial heat and heat from radioactivity, contraction of the Earth due to cooling and release of gravitational energy as the core grows may also be important contributors to the Earth's thermal budget. Thus, even though the relative importance of the various sources of heat is poorly known, there is little doubt that they are sufficient to permit an Earth many billions of years old.

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Another factor that invalidates Kelvin's approach is that convection is a more important mechanism for the loss of heat from within the Earth than conduction. About three-fourths of the heat lost from the Earth leaves through the ocean basins. Virtually all of this heat comes from the mantle and is brought close to the ocean floors by convection. Conduction brings the heat to the surface, where it is lost into space. Approximately two-thirds of the heat lost from the continents is generated within the continental crust by radioactivity. The remaining third is brought to the base of the crust by convection, whereupon it is conducted upward through the crust to the surface. But even though the balance of mechanisms by which heat is transferred from the interior of the Earth outward is known in a semi-quantitative way, current knowledge is insufficient to permit an exact description of heat loss from the Earth.

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Finally, there are other poorly known factors, including the exact composition and structure of the Earth as well as the relevant physical properties of the rocks at various depths, such as conductivity, specific heat, and viscosity. Thus, the thermal history and budget of the Earth are very complicated, and our knowledge of the relevant details remains far too inadequate to permit any valid estimates of the age of the Earth from thermal calculations.

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We know somewhat more now that we did in 1991, but Dalrymples remarks are still pretty much on the money.

Rutherford spoke before the Royal Insitution in 1904, and recalled:

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I came into the room, which was half dark, and presently spotted Lord Kelvin in the audience and realized that I was in for trouble at the last part of my speech dealing with the age of the earth, where my views conflicted with his. To my relief, Kelvin fell fast asleep, but as I came to the important point, I saw the old bird sit up, open an eye and cock a balefule glance at me! Then a sudden inspiration came, and I said Lord Kelvin had limited the age of the earth, provided no new source (of energy) was discovered. That prophetic utterance refers to what we are now considering tonight, radium! Behold! the old boy beamed upon me.

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Copied from The ‘demise’ of Kelvin.

Correct me if I am wrong, but heat cannot be lost into space, except through radioactivity, electromagnetic phenomena (light), or physically projecting material into space (to be lost from that body).Vacuum is an insulator and space is a vacuum.It seems to me much of the "cooling" is about transferring heat from the inner compacted areas (as well as radioactive areas) to outer regions including the hydrosphere and atmosphere.Since we are not creating much light, it would generally be losing atmosphere that would count as the only real "loss" of heat, otherwise it is just a distribution of heat to all parts of the planet.

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holmes
"...what a fool believes he sees, no wise man has the power to reason away.."(D. Bros)"...don't believe I'm taken in by stories I have heard, I just read the Daily News and swear by every word.."(Steely Dan)

We lose a good bit of infrared radiation to space - "light" after a fashion, just not visible. Losses of atmosphere are surely tiny in comparison.

Vacuum essentially prevents the transfer of heat by conduction, which requires molecules that physically touch each other (at least occasionally). Nothing prevents transfer of heat by radiation (not the radiation produced by radioactivity, the radiation produced by all things that are above absolute zero). Note that we receive quite a bit of heat, via radiation, from the Sun ... through the vacuum of space. That warm feeling on your skin at the beach in the summer? Radiation.